Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908302966784000 |
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| author | Oğuz, Ezgi Kantarcı Yıldırım, Emine |
| author_facet | Oğuz, Ezgi Kantarcı Yıldırım, Emine |
| contents | We give two new combinatorial methods for computing cluster expansion formulas for arcs coming from possibly punctured surfaces. The first is by using $T$-walks, an extension of the $T$-path model for unpunctured surfaces to general surfaces. We also introduce a new way of generating $T$-paths. The second method is by using order ideals of labeled posets associated to arcs. We also use the theory of oriented posets to give a quick way to calculate the expressions using $2$ by $2$ matrices. The techniques introduced are applicable to different settings in cluster algebras and beyond. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08011 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations Oğuz, Ezgi Kantarcı Yıldırım, Emine Combinatorics We give two new combinatorial methods for computing cluster expansion formulas for arcs coming from possibly punctured surfaces. The first is by using $T$-walks, an extension of the $T$-path model for unpunctured surfaces to general surfaces. We also introduce a new way of generating $T$-paths. The second method is by using order ideals of labeled posets associated to arcs. We also use the theory of oriented posets to give a quick way to calculate the expressions using $2$ by $2$ matrices. The techniques introduced are applicable to different settings in cluster algebras and beyond. |
| title | Cluster Expansions: T-walks, Labeled Posets and Matrix Calculations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2211.08011 |